In this thesis, a novel compositional multidisciplinary uncertainty analysis methodology is presented for systems with feedback couplings and model discrepancy. The approach incorporates aspects of importance resampling, density estimation, and Gibbs sampling to ensure that, under mild assumptions, the method is provably convergent in distribution. A key feature of the approach is that disciplinary models can all be executed offline and independently. Offline data is synthesized in an online phase that does not require any further model evaluations or any full coupled system level evaluations. The approach is demonstrated on an aerodynamics-structures system, and a comparison to brute force Monte Carlo simulation results is presented. The results demonstrate that our method has captured the joint distribution of interest. This was achieved without any online evaluations of models separately or as a coupled system.
